yTaking Action Book Study: Chapter 7

Chapter 7

Facilitate Meaningful Mathematical Discourse

Reflect:

After reading Chapter 7, please reflect on the questions below and post your response by Monday. Feel free to respond to the questions provided or share something else that you intentionally did differently in regards to facilitating meaningful math discourse.

Please note: the prompts below are to help you reflect. There is not an expectation for you to respond to all {or even any} of the provided questions!

Respond:

Planning for Mathematical Discourse

Choose a task that has the potential to elicit multiple solution paths from your students. The task should engage students in "doing mathematics" {see chapter 3} and allow for use of multiple representations {see chapter 6}. Clearly list the goals that detail the mathematics students will be learning in the lesson.
Anticipate the solution paths, both correct and incorrect, that students might use in working on the task, and prepare assessing and advancing questions to use while monitoring their work.
Decide on a possible sequence of solution paths that you might use during the whole-class discussion of the task, and make note of purposeful questions for connecting student approaches to the targeted mathematical ideas.
Teach the lesson and reflect on how your careful planning helped you manage and facilitate meaningful mathematical discourse that more purposefully moved students toward the intended learning goals.

Interact:

On Tuesday, read your colleagues' reflections and respond to at least one other post by sharing a comment, insight, or interesting possibility by Friday.

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shawnseeleydotcom 44p · 263 weeks ago

Before I read Chapter 7, I worked to plan and create a performance task for an observation activity where Patty and Jerry got to watch students work through a rich task. Prior to creating the task, I decided on learning goals that would drive the task, selecting, sequencing, and discussion.

Learning goals:
1. Understand the difference between area and perimeter. Area represents the number of square units of measure inside of a figure, while perimeter represents a number of linear units of measure along the outside edges of a figure.
2. Understand that there is a relationship between area and perimeter. For any given perimeter, there can be multiple different areas. Changing the structure of the perimeter does not change the overall perimeter, but it may change the overall area.
3. Understand that larger units of measure can be expressed in smaller units of measure, as well as the opposite. For example, 1yd=3ft and 3ft=1yd.
4. Understand that for any given perimeter, the largest possible area will be a square. For example, with a perimeter of 36, a 9*9 square will create an area of 81 square units.

I selected and sequenced student work this way:
1. Misinterpreted the perimeter for area
2. Created rectangular areas that used the entire perimeter, but not the largest area (squares)
3. Largest area possible using front yard fencing for all sides (9*9) and a few strategies to show this
4. Other areas (one side of existing fence or using a corner)

During the lesson, students were engaged (almost) the entire time. After about 20 minutes of student pair work, I called students together and we had a discussion. This was a very productive use of class time and I’m hoping I’ll get a chance to do this again this year.

Here’s a link to a folder that has much of the work I did, along with some anticipated solutions, advancing and assessing questions, and an editable template so you can customize it if you’d like: Dog Run PT

1 reply · active 263 weeks ago

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Meribeth Rowe · 263 weeks ago

What a great PT for your students! What I appreciated in looking through the lesson and slides was how closely you linked the information from chapter 7 and the assessing/advancing questions from the previous chapter. The editable template will save me some time as I begin considering anticipated solutions, question needs for my students and ordering the student samples to share as was done with the Walking Home From School task in the Taking Action book. Thanks Sean!

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Meribeth Rowe · 263 weeks ago

I read chapter 7 back in Early January as I was healing from oral surgery. Having been on some pain medication back then necessitated a second reading just a few days ago. It was during this second reading that I realized why I love teaching math in particular. The power of well planned mathematical discourse for partners, in whole class format and in written communication has the ability to meet the needs of students at all levels of understanding. Don't we live for those moments when a student says, "Oh, now I get it!" or " That's a cool way to solve it!"? The visual on page 150 where the Five Practices of Orchestrating Productive class Discussions will be copied and posted in my room as a reminder of this powerful tool.

Keeping the unit goals/standards visible as teachers make decisions as to which student samples to sequence, share and connect to the goals as described on pages 169-170 made so much sense to me! Although I didn't sequence the student samples in the same order as suggested by the book, I did select the same samples to share as they clearly represented the goals to be achieved. This was a fun chapter!

I plan to use the Walking home from school task with a fifth grade IEP student that I tutor after school. I can then use some of the student samples from the book to promote a discussion around similarities, differences used in the representations provided. I know it won't have the same impact from a discussion perspective without peers but I am curious to practice using assessing and advancing questions with this student.

3 replies · active 259 weeks ago

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shawnseeleydotcom 44p · 262 weeks ago

Meribeth,

I also have read the chapter before and was glad to have reread it :). Isn't teaching math the greatest?

Although I'm much more new to teaching than several of my more experienced coworkers who have likely already had much experience with learning goals and standards, I appreciated the authors consistently drawing attention to the fact that we must use the standards and learning goals as the driver for our tasks. Keeping learning goals based on standards in front of me at all times allows me to better create/select a task that meets the needs of my students, and it allows me to better assess their progress in those standards. This book, along with its predecessor (Principles to Actions) and The Five Practices in Practice, have helped me better think through my planning and instruction.

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Stephanie Clement · 260 weeks ago

Hi Meribeth! I agree about the importance of sequencing student samples. I am eager to be more intentional about this. I think it can be so beneficial for their thinking.

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Caty Carino · 259 weeks ago

Hi Meribeth,

I love your thoughts on sequencing and I love that you are taking time to plan it. I think with more practice sequencing will get easier.

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Stephanie Clement · 260 weeks ago

After reading chapter 7, I’ve learned a lot about the importance of using the five practices in orchestrating productive class discussions when planning my lessons. I’m pretty good at “anticipate” and plan for student responses and questions. I’d like to be more intentional with the other four practices. In Ms. Chavez’s lesson, I really liked how she asked questions and then had the kids explaining their thinking by not only using words, but by explaining their thinking with models. I also really like the idea of creating classroom norms for mathematics discourse. This can really help with class discussions when it comes to respect and the expectations of participation. I’m excited to try this out next year!

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Caty Carino · 259 weeks ago

After reading chapter 7, it really made me reflect on what mathematical discourse was happening in my classroom and how I need a bit of makeover in that department. I love this book because it does get me excited to try new things and ways to make my math time more safe environment to learn and where other are benefitting from learning from each other, rather than always just learning from myself. I loved the idea when sharing is that it is more of a conversation amongst peers. I would love to incorporate this more into my classroom, because I do feel when I call on someone to share I am having the conversation with the student. But if it was where peers were having the conversation I know my engagement level would increase.

2 replies · active 253 weeks ago

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Susan Heater (TSD) · 255 weeks ago

I agree with you about the conversation among peers. Instead of using it solely for formative feedback, it can be used to allow kids to collaborate, and help them stay more engaged in the lesson!

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Julie Rodriquez · 253 weeks ago

Caty, I want to work on that last piece you mentioned, too - creating conversations that are happening among peers rather than between the student who is sharing and myself. Maybe we can discuss this more for next year and support one another/collaborate? It would be great to hear what you are trying in your classroom and what is working and what isn't. I bet Madison would love to be a part of that conversation, too!

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Susan Heater (TSD) · 255 weeks ago

Chapter 7 has been the most meaningful for me. I think mathematicacl discourse is so important and it has been a focus of mine this year. I love when they bring up the times Mr. Harris brings up partner talk and mention that they did not work on a task during this partner time, but rather had students clarify, explain, and share their ideas and work.They state on page 147, "This allowed students to clarify their understanding of the problem situation in the task" and also allowed them to get ideas about how to solve the problem based on what their partner shared. The 5 practices in orchestrating productive class discussions was also a different way for me to think about class discussions. What I want to implement in the coming school year is written communication about math. One of my teammates has journals that her kids write in for math every day, and I would like to follow suit because she raves about the ability for kids to think through problems and slow down their thinking process.

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Julie Rodriquez · 253 weeks ago

The building of a classroom community in which the students share the responsibility of communicating and learning math takes a lot of work and guidance. But I do believe it is worth it. And do I know that this is an area that I know needs growth in my teaching. I loved the idea of videotaping a class discussion and charting student responses so that students are made more aware of their contribution (or lack of). Then brainstorming and developing a set of expectations that students are responsible for upholding would be very valuable. I think one part that is missing when I try to create a set of norms for class discussions is the opportunity for students to develop and then reflect on their self-created norms. In the past, I have been the one who gives the students a set of expectations (and yes, sometimes they help create them) but the student ownership is missing.

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